In the particular case of the dynamics and optimisation of vein networks in Physarum, several modelling approaches aiming to explore the formation and optimisation of network paths have been introduced, [1]}. These approaches were based on the phenomenology of Hagen-Poiseuille flows in graphs, and optimisation has been introduced by controlling channel conductivity through ad hoc local evolution laws, together with stochastic actualisation processes. These models converge to steady network paths, which, in some cases, are close to Steiner tree type of connections, [2]} and [3]}, or even shortest path solutions [4]}, [5]}.
